Question

for the year, brunos monthly dining - out expenses were: $200, $220, $210, $230, $210, $205, $215, $225, $210, $205, $230, and $220. what is the standard deviation of his expenses, rounded to the nearest whole number? use the following formula to calculate standard deviation: $\sigma=sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\text{mean})^{2}}{n}}$ where $x_{i}$ is each data point, and $n$ is the number of data points. notice that $\sum_{i = 1}^{n}(x_{i}-\text{mean})^{2}=1,100$. $12.34 $11.25 $8.54 $9.57

Explanation:

Step1: Identify number of data - points

There are 12 data - points, so $n = 12$.

Step2: Use the standard deviation formula

Given $\sum_{i = 1}^{n}(x_{i}-\text{mean})^{2}=1100$ and the formula $\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\text{mean})^{2}}{n}}$, we substitute the values: $\sigma=\sqrt{\frac{1100}{12}}$.

Step3: Calculate the value

$\frac{1100}{12}\approx91.67$, and $\sqrt{91.67}\approx9.57$.

Answer:

$\$9.57$